I have been to Dollywood three times in the past few years, and in my opinion it is more like BGW than KD. It has a country/mountain theme with a Christian vibe. Generally, I believe people who love BGW tend to like Dollywood, as well, because it is a similar type of park.
There is a children's area called "Country Fair." There are also a coal-powered train and some other kid-friendly attractions.
Despite the park's reputation for fantastic food, I was honestly a bit underwhelmed. That said we did find several places that we really enjoyed. The Grist Mill in particular is worth a stop. The cinnamon bread is amazing, and the water wheel and mill are super-cool.
I've only been to one of the shows at Dollywood, but it was very good by theme park standards. I liked it a lot more than anything at BGW.
There are several charming shops, and the area is very wooded. So, walking around the park is pleasant, as well.
The first time we went, Dollywood seemed run down. In fact there was mold in one of the bathrooms, and the customer service was terrible. This past year, however, it seemed greatly improved. It was cleaner and the staff was incredibly friendly.
I, personally, don't like the water park, because the water was much too cold for me.
DreamMore, the new resort hotel, however, was fantastic. When we went for the holiday event, our park tickets and front of the line Q-bot were included with room. We also had a complimentary shuttle to the park, so we didn't have to pay for parking either.
Hope that helps?